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Common Notion 1

Common Notion 1
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2020-04-22 23:20
TriangleAngleGeometric Construction
In collections Basic Constructions
This example demonstrates Common Notion 1, which states that the whole is greater than the part. Key mathematical concepts include geometric construction and equality. Using GeoGebra commands such as Segment, Distance, Point, and Angle, the example constructs figures that satisfy Common Notion 1. Suitable for middle school and above students to learn geometric construction and equality.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Distance(A, B) → distanceAB
  3. Point(Circle[C, distanceAB]) → D
  4. Segment(C, D) → g
  5. Distance(C, D) → distanceCD
  6. Segment(E, F) → h
  7. Segment(F, G) → i
  8. Angle(G, F, E) → α
  9. Rotate(H, α, I) → H'
  10. Angle(H, I, H') → β
  11. Segment(H', I) → j
  12. Segment(H, I) → k
  13. Polygon(J, K, L) → t1, l, j_1, k_1
  14. Angle(L, K, J) → γ
  15. Angle(J, L, K) → δ
  16. Distance(K, L) → distanceKL
  17. Point(Circle[M, distanceKL]) → N
  18. Segment(M, N) → m
  19. Rotate(N, γ, M) → N'
  20. Angle(N, M, N') → ε
  21. Rotate(M, (-δ), N) → M'
  22. Angle(M', N, M) → ζ
  23. Line(M, N') → n
  24. Line(N, M') → p
  25. Intersect(n, p) → O
  26. Segment(O, M) → q
  27. Segment(O, N) → r

AI Drawing Prompt Reference

Draw a triangle ABC, then take a point D on BC such that BD equals CD. Next, draw a circle with center C and radius CD, intersecting AB at point E. Connect DE, then draw a circle with center D and radius DE, intersecting BC at point F. Connect EF, then draw a circle with center E and radius EF, intersecting AB at point G. Connect FG, then draw a circle with center F and radius FG, intersecting BC at point H. Connect GH, then draw a circle with center G and radius GH, intersecting AB at point I. Connect HI, then draw a circle with center H and radius HI, intersecting BC at point J. Connect IJ, then draw a circle with center I and radius IJ, intersecting AB at point K. Connect JK, then draw a circle with center J and radius JK, intersecting BC at point L. Connect KL, and finally draw a triangle JKL.
The prompt above was compiled from the original drawing commands and is for reference only.